Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
508 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10617163 | C2 | semidirect |
| 3. #10604598 | C2 | semidirect |
| 4. #10604593 | C2 | semidirect |
| 5. #10604420 | C2 | semidirect |
| 6. #10598590 | C2 | semidirect |
| 7. #10598585 | C2 | semidirect |
| 20. C5×#459 | C4 | semidirect |
| 23. #65361 | C4 | semidirect |
| 24. #65297 | C4 | semidirect |
| 25. #65131 | C4 | semidirect |
| 150. #459 | AGL(1,𝔽5) | semidirect |
| 405. C5 | #9163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617163 | 2 |
| #10612045 | 2 |
| #10604598 | 2 |
| #10604593 | 2 |
| #10604420 | 2 |
| #10598590 | 2 |
| #10598585 | 2 |
| #9163 | 5 |